maths based riddles... See if you can answer them.

[micky g]

I get it to be the same?

[Dr Jekyll]

I think they are both the same, but I'm no mathematician so am open to persuasion.

Incidentally the reason the plane on conveyor belt debate never dies is that the universe is divided into 2.

Half the sentient beings think it's a question about whether the plane can take off without airspeed, the remainder know it's actually a question about whether the plane will move and therefore gain airspeed. So they argue about 2 totally different things and can never resolve it.

[Dr_Gonzo]

micky g said:

I get it to be the same?

That's what I get too.

[Alfanatic]

K87 said:

Dr Jekyll said:

You have a jug of milk and a jug of black coffee.

You take a spoonful of milk from the milk jug, pour it into the coffee, and stir thoroughly.

You then take a spoonful from the coffee jug and pour it into the milk jug.

Do you end up with more coffee in the milk or more milk in the coffee?

More milk in the coffee as the spoon taken from the coffee will contain a tiny amount of milk whereas the spoon taken from the milk was all milk to start with.

Terrible explanation but pretty sure it's right

I think there's a trick here. because you take the milk first, you are adding more pure milk to the coffee, indeed, but you are also removing more milk from the milk jug. When you do the opposite, you are adding less coffee to the milk jug because of the milk content, but you are also removing less coffee from the coffee jug.

I haven't done the maths yet but I'd guesstimate you'd end up with the same percentage of both.

OK, my rudimentary maths says that the first person who said the mixtures are the same (but opposite.. .you know what I mean) is correct.
Like this:

Assuming jug holds 100ml and spoon holds 10ml to keep the maths simple:

Start with 100ml milk in milk jug, 100ml coffee in coffee jug
Transfer 1 spoon milk to coffee jug.
Milk jug now has 90ml milk, coffee jug has 100ml coffee and 10ml milk

Transfer 1 spoon mix from coffee jug to milk jug
The mixture is 90.9% coffee, so the spoon has:
9.09ml coffee, 0.91ml milk.

So, the final tally:

Milk jug:
90.91ml milk, 9.09ml coffee

Coffee jug:
90.91ml coffee, 9.09ml milk

Edited by Alfanatic on Tuesday 16th August 13:25

[Megaflow]

Max_Torque said:

Your girlfriend/wife/female partner says

"look, my new pair of shoes were a bargain, only cost £350"

Resolve the equation, showing all your working, that mathematically demonstrates why any attempt to argue or comment about the relative magnitude and vectors of "a bargin" will result in "the doghouse" regardless of the actual starting node condition. (extra points will be awarded for an accurately filled in "Truth table" for said scenario)

I reckon this about covers it:

Edited by Megaflow on Tuesday 16th August 13:35

[RizzoTheRat]

How about a slightly physics based one then

You have a glass of water with an ice cube in it. The ice melts. What happens to the water level?

[Alfanatic]

RizzoTheRat said:

How about a slightly physics based one then

You have a glass of water with an ice cube in it. The ice melts. What happens to the water level?

It goes down slightly due to general evaporation. The melting ice in itself does not change the water level.

[bishbash]

RizzoTheRat said:

How about a slightly physics based one then

You have a glass of water with an ice cube in it. The ice melts. What happens to the water level?

does it drop? There's usually some air bubbles in ice?

[syko89]

does it rise by the volume of ice above the water level?

[RizzoTheRat]

Alfanatic said:

It goes down slightly due to general evaporation.

If you're going to that level of detail you forgot to include the start and end temperatures of the water to account for contraction/expansion

[Macd355]

It drops, since ice is less dense than water?

[K87]

Hmm can't put my finger on it but it's something to do with the different densities of the ice and water so when it's ice it's displaced by the volume of the ice, but when it melts it's displaced by the mass of the new water which is less so the water level falls.

Or something to that effect, similar to the mass in a boat on a lake.

[weeredmetro]

Alfanatic said:

The melting ice in itself does not change the water level.

This, as long as the ice cube was floating to start with.
If the ice cube was somehow trapped underwater, when it melts, the level would drop as liquid water takes up less space than ice

[Dr Jekyll]

The water level stays the same. Anything floating displaces it's own weight in water, which for an ice cube is the same volume as the cube when melted.

[Alfanatic]

K87 said:

Hmm can't put my finger on it but it's something to do with the different densities of the ice and water so when it's ice it's displaced by the volume of the ice, but when it melts it's displaced by the mass of the new water which is less so the water level falls.

Or something to that effect, similar to the mass in a boat on a lake.

Density decides whether it floats or not, and how much pokes above the surface. Mass determines how much water it displaces. The mass doesn't change. If it's 50g of ice, it displaces 50g of water and makes a hole in the water that would hold...50g of water. When it melts, it becomes 50g of water. The icecube itself does indeed take up less volume, but the water level stays the same because while only 9 tenths of the icecube could fit in the hole it was making, 10 tenths of the water that makes the ice cube fits.

In other words, the volume of the system has gone down if you also take the ice cube's volume into consideration, but the water level does not move.

So, imagine you could remove the icecube but stop the water from flowing (without freezing it) so that it doesn't change shape and you have a hole shaped like the icecube on the surface.

Melt the icecube, and the water you get from that will be exactly enough to fill the hole, no more, no less.

When you launch a boat, you are adding the mass of the boat to the system. The lake's water level will rise, very slightly, by a level which, when multiplied by the lake's surface area, would give you a volume of water with the exact mass of your boat.

Similarly, when you first launch your icecube by dropping it in a glass of water, the water level will rise. As long as that extra mass then stays in the glass of water, as ice or as water it doesn't matter, the level will stay the same.

Edited by Alfanatic on Tuesday 16th August 14:22

[carmonk]

I've always wondered why melting an ice cube in a glass doesn't raise the water level but melting an iceberg at the poles apparently would...

[marksx]

Because not all the polar ice is in the water already?

[K87]

Alfanatic said:

Density decides whether it floats or not, and how much pokes above the surface. Mass determines how much water it displaces. The mass doesn't change. If it's 50g of ice, it displaces 50g of water and makes a hole in the water that would hold...50g of water. When it melts, it becomes 50g of water. The icecube itself does indeed take up less volume, but the water level stays the same because while only 9 tenths of the icecube could fit in the hole it was making, 10 tenths of the water that makes the ice cube fits.

In other words, the volume of the system has gone down if you also take the ice cube's volume into consideration, but the water level does not move.

So, imagine you could remove the icecube but stop the water from flowing (without freezing it) so that it doesn't change shape and you have a hole shaped like the icecube on the surface.

Melt the icecube, and the water you get from that will be exactly enough to fill the hole, no more, no less.

When you launch a boat, you are adding the mass of the boat to the system. The lake's water level will rise, very slightly, by a level which, when multiplied by the lake's surface area, would give you a volume of water with the exact mass of your boat.

Similarly, when you first launch your icecube by dropping it in a glass of water, the water level will rise. As long as that extra mass then stays in the glass of water, as ice or as water it doesn't matter, the level will stay the same.

Edited by Alfanatic on Tuesday 16th August 14:22

Got it!

Is the %age of ice that sticks out of the water the same as the %age difference between the density of the two?

[carmonk]

marksx said:

Because not all the polar ice is in the water already?

I really meant the North Pole. Icebergs are in the sea and there's no land at the North Pole so why would melting affect sea levels?

[K87]

carmonk said:

marksx said:

Because not all the polar ice is in the water already?

I really meant the North Pole. Icebergs are in the sea and there's no land at the North Pole so why would melting affect sea levels?

Because only what's above the sea level is currently melting? Once the ice below the surface melts it should fall back to the original level?